On the use of Hadamard matrices in factorial designs

Abstract

Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. It is of practical interest for a given k to know all the inequivalent projections of the design into the k dimensions. In this paper we discuss the application of Hadamard matrices as screening designs. In particular, we study all the inequivalent projections of inequivalent Hadamard matrices of orders 16, 20 and 24 into k = 3, 4 and 5 dimensions. Then we sort them using the generalized resolution, generalized aberration and uniformity criteria. We also present an illustrative example of the projective properties of Hadamard matrices using a simulated experimental situation with 20 runs.